Generally, fighting styles can be broken down into 5 categories:

Anything-Goes Style refers to the school of martial arts practiced by the Tendos and the Saotomes. Unless otherwise specified, these are
the only two families in the world who practice this style of martial arts,
passed down from its originator and master, Happosai. The Anything-Goes style is one of the most flexible styles of martial arts, able to adapt to any situation and always open to change or revision. A
"Revised" technique can be created almost on the spot, as can any
other new techniques. This lack of structure is its greatest strength (and
also, perhaps, its greatest weakness).

Chinese Martial Artists are those martial artists in the series whose styles originate from China or who trained in China. This includes the Chinese Amazons, as well as anyone else who received basic training there. Chinese styles vary in method and name, so it is difficult to pinpoint any generalities in technique.

Freestyle refers to martial arts styles that have been improvised or enhanced from "normal", Karate/Kenpo based moves. These particular styles use unique objects, methods, and weapons in order to defeat their opponents. This is the most inclusive category since there are a variety of "improvised" or innovative styles in Ranma 1/2.

Power Players are martial artists who may or may not use traditional styles - however, their power is potentially immense, usually based on energy or chi-based attacks. These martial artists are more liable to use their advanced power and stamina to beat their foes rather than any real finesse or style of attack.

Miscellaneous refers to any other martial artists who don't fit in the above four categories.